１８ Quantum Mechanics

１８−１ What is Quantum mechanics？
○Energy, length, speed, and time, those physical quantities have the smallest unit(quanta) that can not be divided any more.

○About the particles like the size of electron (: 2.8 × 10 ^ -15m), you can see the state (the value of the energy), if you get the wave function by solving the wave equation (Schrodinger equation: partial differential equation 1926) , or if you solve the equation of motion of the Heisenberg (the determinant 1925) .
※The wave equation and the equation of motion of Heisenberg is mathematically equivalent.

○The Wave equation
• The Wave equation is a Fundamental equation of quantum mechanics. It is contrasted with Newton's equation of motion of classical mechanics.
・We can calculate the state of the matter wave stochastically by the equation.
・The Wave equation cannot be obtained strictly by using classical mechanics or mathematics. It is the equation that successfully describes the physical phenomena.
※Relativity is classical mechanics.： reduced Planck constant
ｔ：time
ｍ： mass of particle
Ψ（Psi）：wave function： Complex quantity, which was introduced to represent the wave
X：position
V： potential energy

○The squared modulus of the wave function is a real number interpreted as the probability density of measuring a particle's being detected at a given place.
・The figure below shows the graph of the probability density and the energy state of matter. [1]
※The red line is the energy state(n). The probability density and n is changed at intervals.

☆The universe had particles that have exactly the same properties without limit, at energy following the mathematical rules!

○The universe was born from a quantum fluctuation.

○Wave function is a function of the complex because the wave equation contains complex number. [2]
・・・The universe is represented by imaginary!

１８−２ Material Wave（de Broglie wave）
○On a submicroscopic level, there is no boundary strict between particles and wave.
→When existence is regarded as a wave motion, in physics, it is called a "place." For example, light is wave motion of an electric field and magnetic field.

※ It is under a very microscopic situation like an electron beam that the character as a wave is actually observed.
※ It is impossible to determine the size of the electron.
※ And the length of orbit around the nucleus is an integer multiple of the wavelength (10 minus 10 square m).
＝Why the electrons are not getting stuck in the nucleus.

○The image of the wave of complex number [1]
※Whole wave represents one of the particles.
※Height and depth of the wave corresponds to the size of the wave function.
：de Broglie wave＝the wave function